Related papers: Minimax Signal Detection Under Weak Noise Assumpti…
We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…
We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…
This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting introduced in (IEEE Trans. Inform. Theory…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
The CSL model predicts a progressive breakdown of the quantum superposition principle, with a noise randomly driving the state of the system towards a localized one, thus accounting for the emergence of a classical world within a quantum…
In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…
This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned…
This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
The method of location and spectral estimation of weak signals on a noise background is being considered. The method is based on the optimized on order and noise dispersion autoregressive model of a sought signal. A new approach of model…
We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
We provide the asymptotic minimax detection boundary for a bump, i.e. an abrupt change, in the mean function of a stationary Gaussian process. This will be characterized in terms of the asymptotic behavior of the bump length and height as…
We consider parameter estimation under sparse linear regression -- an extensively studied problem in high-dimensional statistics and compressed sensing. While the minimax framework has been one of the most fundamental approaches for…
System identification is a fundamental problem in control and learning, particularly in high-stakes applications where data efficiency is critical. Classical approaches, such as the ordinary least squares estimator (OLS), achieve an…
The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…